It is a curious feature of contemporary analytic philosophy, which takes some getting used to, that its practitioners tend to explain things in terms of the more poorly understood. Thus, for instance, they like explaining things in terms of propositions, even though there is no generally accepted account of what propositions are; and they like appealing to intuitions, even though there is no particularly illuminating account in contemporary analytic philosophy of what intuitions are; and they like analyzing things in terms of their properties despite the fact that there is no widely accepted account of what properties are; and they like boiling things down to justification even though they can't agree on what justification is or implies; and they like bringing in identity despite the well-known puzzles concerning it; and so forth. I see that Andrew Moon has recently been puzzling about one of these curious terms, 'occurrent belief', in a recent "Certain Doubts" post.
It's worth thinking a moment about the history of the phrase, which shows exactly why it falls into this category. 'Occurrent belief' arose from the dispute over the nature of beliefs in the middle of the twentieth century, which was regularly -- especially by dispositionalists -- put in terms of occurrentism vs. dispositionalism. Roughly speaking, dispositionalists took 'belief' to mean a state one is in over a period of time, not any kind of happening or doing. Pretty much any account of belief that did not make belief a disposition was labeled occurrence theory of belief, since the dispute was mostly ginned up by dispositionalists to build arguments for dispositionalism, and they just stuffed all their very different opponents in one box to do it. The dispute faded, more or less, although dispositionalism won to the extent of getting to set the default terminological assumptions among philosophers, but the terms remained; when people talked about 'occurrent belief' they meant simply 'belief as it would be understood in some occurrence theory or other'. 'Occurrent belief', in other words, never did more than signal that the person using it was not using 'belief' as a dispositionalist would use the term; it never indicated anything about what that belief was.
Of course, in particular cases we can find particular accounts of belief in play, further specifications from context, or because people wanted to be clear what they meant when using the phrase. But such cases simply show that 'occurrent belief' largely meant whatever people wanted it to mean. A common early view was that occurrent beliefs were acts of some kind; e.g., acts of assent or taking an attitude toward propositions. We find trace of this, for instance, from a dispositionalist perspective, in Price's influential Gifford Lectures. Another, later, example of this view would be Amelie Rorty's definition of it as the assertion or denial of propositional content. A different view that sprang up, somewhat later, but now quite common, was the one that occurrent beliefs were just beliefs-we-are-conscious-of-somehow; David-Hillel Ruben says somewhere, for instance, that as far as he can tell it's the only plausible meaning of the phrase. The two are obviously going to be capable of having radically different implications. In reality, of course, people just use the phrase with occasional clarification when necessary, to mean whatever it is convenient for it to mean at the point when they are using it.